Measurements of the Influence of Integral Length Scale on Stagnation Region Heat Transfer

Abstract

The purpose of the present work was twofold: first, to determine if a length scale existed that would cause the greatest augmentation in stagnation region heat transfer for a given turbulence intensity and second, to develop a prediction tool for stagnation heat transfer in the presence of free stream turbulence. Toward this end, a model with a circular leading edge was fabricated with heat transfer gages in the stagnation region. The model was qualified in a low turbulence wind tunnel by comparing measurements with Frossling′s solution for stagnation region heat transfer in a laminar free stream. Five turbulence generating grids were fabricated; four were square mesh, biplane grids made from square bars. Each had identical mesh to bar width ratio but different bar widths. The fifth grid was an array of fine parallel wires that were perpendicular to the axis of the cylindrical leading edge. Turbulence intensity and integral length scale were measured as a function of distance from the grids. Stagnation region heat transfer was measured at various distances downstream of each grid. Data were taken at cylinder Reynolds numbers ranging from 42,000 to 193,000. Turbulence intensities were in the range 1.1 to 15.9 percent while the ratio of integral length scale to cylinder diameter ranged from 0.05 to 0.30. Stagnation region heat transfer augmentation increased with decreasing length scale. An optimum scale was not found. A correlation was developed that fit heat transfer data for the square bar grids to within ±4%. The data from the array of wires were not predicted by the correlation; augmentation was higher for this case indicating that the degree of isotropy in the turbulent flow field has a large effect on stagnation heat transfer. The data of other researchers are also compared with the correlation.